Question

A metallic cube has a resistance 9$\Omega$. It is now cut into 27 smaller identical cubes. The resistance of each smaller cube is :

• A. 1/3$\Omega$
• B. 27$\Omega$
• C. 18$\Omega$
• D. 3$\Omega$

Answer 1

The correct option is B 27$\Omega$

Resistance of the original metallic cube is given by,

$R_C=\frac{\rho L}{A}=\frac{\rho L}{L^2}=\frac{\rho }{L}=9\Omega$ ..(given)

After cutting the cube in to 27 smaller cubes the length of the smaller cube becomes $\frac{L}{3}$

$\therefore$ The resistance of the smaller cube is given by,

$R_c=\frac{\rho L/3}{a}=\frac{\rho L/3}{L^2/3^2}=\frac{\rho }{L/3}=3\times \frac{\rho }{L}=3\times 9\Omega =27\Omega$